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Mathematicians Solve the Mystery of Traffic Jams
mlimber writes "Do you ever find yourself in a traffic jam, thinking, 'Man, there must be a bad accident up ahead,' but as you plod along you see no evidence of any crash? Some mathematicians have solved the mystery by developing a mathematical model that shows how one driver hitting the brakes a little too hard can cascade into a backup miles behind. The mathematicians' future research will investigate how automatic braking systems may alleviate the problem."
One of the most irritating driving habits I can think of are people who obsessively cover the brake every 20-30 seconds or so. Usually soccer moms in Suburbans or elderly in the largest Lincoln they could find. There's nothing ahead of them, no reason really to tap the peddle, but they do it anyway out of habit.
If an automatic braking system can solve this problem, I'm in for my tax dollars.
Eagles may soar, but weasels don't get sucked into jet engines.
The difference is the overall level of asshole-ness of the drivers. Much of the braking in dense traffic is caused by desperate maneuvers. In New York, the maneuvers are caused by the fact that I'd say less than 10% of the drivers will allow anyone to merge ahead of them for ANY reason. In dense traffic moving at 50mph, it's not uncommon to be within 3-4 meters of the car in front of you, or even less. And since nobody will allow you to merge, you're forced to perform pretty daring high-acceleration maneuvers to force yourself into the target lane... which will cause that lane to rapidly decelerate, clearly creating the traffic wave.
All it would take to stop this from happening, is for people to stop being assholes, and to let you through, when you're trying to get into an exit, 1/4 mile away.
Not necessarily stupidity. if I can see past the driver in front of me, I can make a better decision. I can see that he is simply adjusting speed to allow for a more reasonable space between him and the car in front. If I am stuck behind an SUV in my car, then I am not sure if his tap on the brake is about to turn into a full fledged stomp of the brakes, and I have to adjust, and possible harder that I need to. This becomes a cascading event.
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Another cause for bad traffic is the ridiculously easy driving test we have in the States. Couple that with law-enforcement only ticketing speeders instead of bad drivers in general, and you get the traffic we have in most of our cities. I also hate how all accidents are chalked up to "failure to control speed", which makes it sound as if speeding were the main cause of all accidents. In reality, failure-to-yield is overwhelmingly the #1 cause of collision accidents, not speed. But the revenue hungry cops would rather sit on their motorcycles with radar guns than actually pull people over for changing 5 lanes at once, or cutting off other drivers by pulling out in front of them and then NOT accelating.
Not to mention, hell will freeze over before they ever ticket a slow driver in the left lane.
The effect would be mitigated if everyone would refrain from following other cars so closely.
Yeah.... I tried this for several weeks. Except everyone took the opportunity to sneak in front of me so they could play a game of changing lanes repeatedly to snake their way through traffic faster.
That is the problem. You can do what is best for the group, but then selfish individuals abuse that for their own gain which hurts the group more. I can't wait until we have self driving cars... I could easily foresee traffic signals going away, much more efficient cars and no more worrying about getting to old to be safe on the roads. Add to this a dropped death rate, and this breakthrough would easily be the greatest advancement of the 21st century.
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It is absolutely freakin impossible!
If I give 2 seconds to the car ahead, it is likely that two drivers and maybe a third idiot will wedge into that gap. Now I have to slow down to achieve the new two second gap, which will cause everyone behind me to react with breaking and more slowdowns. Eventually there will be a wave of breaking that causes a huge delay in traffic with no apparent cause. I may even be lucky enough to be run into from behind, and then 2 seconds at zero mph would be the exact lack of distance between our now entangled bumpers.
Now if we could actually give space to everyone and not have the self-righteous take advantage of these gaps as there way to shave 8 seconds off of their commutes you may have a point.
Sorry to be cynical to your point, but I live in Atlanta, and people here suck.
Yeah, but when you start giving enough room between you and the car ahead, an idiot besides you speeds up and steals your place
Conclusion: Traffic jams are caused by idiots.
Apparently, a lot of people think that their vehicles only have "stop" and "go" modes, without multiple different levels of coasting and slowing down without the brakes for those minor adjustments. I'll take my car out of overdrive quite often to adjust just a bit, rather than hitting the brakes needlessly. That way when I hit my brakes, I actually mean it. Brake lights = slowing down non-trivially. I wish more people did that.
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Yeah, but when you start giving enough room between you and the car ahead, an idiot besides you speeds up and steals your place
Conclusion: Traffic jams are caused by idiots. Well of course, that's because it's a race, they HAVE to be in front of you, they HAVE to get to the next red light before you.
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I tend to do this during heavy traffic. I drive a manual, and shifting in and out of gear over and over gets old real fast. The trick is just to not care. It's hard, I know. Give yourself more than 2 seconds. I tend to go by car lengths, just because traffic conditions vary. In slow traffic (5-25 mph) I'll try to maintain a 10-car-length space or so. This doesn't mean I'm constantly braking and accelerating; if I wanted to do that, I'd just tailgate the guy in front of me like everyone else. If someone cuts in in front of you, let them. They're probably just going to speed up and slam on their brakes when they get to the car in front of you. You can slightly adjust your speed by releasing the gas pedal a little to maintain your space. There's no real hurry -- you have 9 car lengths worth of time to do this. If traffic is heavy and slow enough, you end up with people to the right and left (and behind) you who aren't "cheaters," and people tend to stop cutting in front of you so much. But even if they do, the magic phrase is: "who cares?"
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Is it idiotic to do what is best of your own self interest? The answer is more complicated than you might think, it depends upon what your adversaries do. This situation sounds very similar to the prisoners dilemma or indeed any other situation where individuals acting in their own self interest collectively reach a worse result (for each of them individually) than would otherwise have occurred if they cooperated instead of taking the greedy approach (i.e the Tragedy of the Commons).
Because people aren't smart enough to do that. You see the same people who will do 40mph up to a red light just to sit there. I on the other hand try to guess when the light is going to change and just brake a little, so that I hit the intersection just when it turns green and still have some momentum left saving myself some fuel and time. People just don't think about what they're doing, and if you explain it to them they don't listen.
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Courtesy of a course I audited at MIT on discrete mathematics, about 20 years ago, which included a fascinating section on the mathematics of traffic...
(1) They're not really standing waves, which are composed of traveling waves going both forward and backward (and waves can't propagate forward in traffic). They're ordinary traveling waves. The best analogy is to the flow of a compressible gas in a pipe. You can easily get strong shock waves at various densities and flow rates when you introduce obstructions or change the flow rate at various branch points.
Part of the problem in our expectations is that we (unreasonably) expect traffic flow to be more like the flow of an incompressible fluid like water, where, generally speaking, more pressure simply equals faster flow. It's the presence of compressibility that makes gas flow in certain critical regions much more complicated than water flow, so that, for example, an increase in pressure (e.g. an increase in cars entering at a given on-ramp, or a constriction due to an accident) can result in drastic decreases in flow. The compressibility comes about in traffic because the density of cars is quite variable.
(2) Along those lines, the density per se -- the space between the cars -- really has very little to do with the peculiarities of traffic. It's the fact that the density can change locally which makes the "car gas" compressible, and allows for density waves (traffic jams, stop-n-go traffic, etc.).
But the reason the density changes locally is not because people don't leave enough space between their car and the car ahead, but because of human reaction time. If the car spacing (i.e. density) changes here at time t, human reaction time means it cannot propagate very fast -- it will change there at some time t' significantly later than t. That is, a density wave must propagate. Under the right conditions, it's quite easy for such a density wave to grow in amplitude as it goes. Hence, a very small initial perturbation in the density -- one driver slamming on the brakes -- can grow much larger as it propagates, so that at some distance away large numbers of cars must come to a halt.
The only real solution is to make the car "gas" much less compressible, and that requires greatly raising the speed at which density fluctuations can propagate, in other words, tremendously shortening the time it takes for cars to respond to slight changes in spacing. Presumably, that suggests computer control of cars.